Which of the given values of $x$ and $y$ make the following pair of matrices equal

$\left[\begin{array}{cc}3 x+7 & 5 \\ y+1 & 2-3 x\end{array}\right]=\left[\begin{array}{cc}0 & y-2 \\ 8 & 4\end{array}\right]$

If $I$ is a unit matrix, then $3I$ will be

Let $A =\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)$ and $B =\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)$. Then the number of elements in the set $\left\{( n , m ): n , m \in\{1,2, \ldots . .10\}\right.$ and $\left.nA ^{ n }+ mB ^{ m }= I \right\}$ is

$AB = 0$, if and only if

If $A = \left[ {\begin{array}{*{20}{c}}
\alpha &0\\
1&1
\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}
1&0\\
5&1
\end{array}} \right]$ , then the value of $\alpha $ for which $A^2 = B$ is